Pendulum Problem: Potential energy equals? kinetic energy

[smeiste]

Homework Statement

A pendulum consists of an object of mass m = 1.65 kg swinging on a massless string of length l. The object has a speed of 1.97 m/s when it passes through its lowest point. If the speed of the object is 0.87 m/s when the string is at 70° below the horizontal, what is the length of the string?

Correct answer: 2.64 m (to 3 sig figs)

Homework Equations

Ep = mgh
Ek = 1/2mv^2

The Attempt at a Solution

I tried the equation:

mg(length(1-cos20°)) = 1/2mv^2

and this did not work.. it worked when I had the length and needed the velocity?

 

[PeterO]

Homework Statement

A pendulum consists of an object of mass m = 1.65 kg swinging on a massless string of length l. The object has a speed of 1.97 m/s when it passes through its lowest point. If the speed of the object is 0.87 m/s when the string is at 70° below the horizontal, what is the length of the string?

Correct answer: 2.64 m (to 3 sig figs)

Homework Equations

Ep = mgh
Ek = 1/2mv^2

The Attempt at a Solution

I tried the equation:

mg(length(1-cos20°)) = 1/2mv^2

and this did not work.. it worked when I had the length and needed the velocity?

Using your two speeds, you can calculate the kinetic energy at the bottom, and when in the 70 degree position [or indeed 20 degree as you are starting to use]
The reduction in kinetic energy will be accompanied by an equivalent increase in Potential energy - so you know the gain in height.

A bit of trig on the triangle formed should yield the pendulum length you are after.

 

[smeiste]

Thank you so much!